List of top Mathematics Questions on Pair of Linear Equations in Two Variables asked in UK Class X

Two years ago, father was thrice as old as his daughter, and 6 years later he will be 4 years older than twice her age. How old are they now?
Show graphically that the linear equations \( x - y = 8 \), \( 3x - 3y = 16 \) are inconsistent, i.e. it has no solution.
Find the value of K for which the given system of equations has infinitely many solutions: \[ Kx + 3y = K-3 \quad \text{(1)} \] \[ 12x + Ky = K \quad \text{(2)} \]